Most calculations in NISM Series V-A sit in the chapters on NAV and expenses, taxation, risk and return, and scheme performance (7, 8, 10 and 11). Take one of the two free 20-question numerical tests below (you need a free account), then use the formula sheet to fix whatever you got wrong. Scoring copies the real exam: 1 mark for each correct answer and no deduction for a wrong one.
Two free 20-question tests, 40 different calculation questions in all: NAV, expense ratio, exit load, SIP, capital gains tax, returns and risk measures. Every answer comes with the formula, the working and the common mistake when you finish.
NISM does not publish how many questions in each paper are numerical, so use this table as a guide to where calculations appear in the V-A syllabus. The last two columns show how many numerical questions BullWiser has written for each chapter (200 in the full bank, 40 of them in the two free tests).
| Chapter | What gets calculated | Full bank | Free tests |
|---|---|---|---|
| 1. Investment Landscape | Real return, inflation-adjusted values, CAGR, compounding, Rule of 72 | 10 | 4 |
| 2. Concept and Role of a Mutual Fund | Units allotted, applicable NAV, holding value, fund size, ownership | 10 | 4 |
| 5. Scheme Related Information | SIP, SWP and STP arithmetic, IDCW, asset allocation, WAM | 20 | 4 |
| 6. Fund Distribution and Channel Management | Trail and upfront commission, clawback, break-even AUM | 10 | 4 |
| 7. NAV, Total Expense Ratio and Pricing | NAV, TER slabs, exit load, entry/repurchase price, accruals | 40 | 4 |
| 8. Taxation | Capital gains, TDS, set-off of losses, IDCW tax, ELSS | 30 | 4 |
| 9. Investor Services | Redemption interest, folio units, nominee split, average cost | 5 | 4 |
| 10. Risk, Return and Performance of Funds | HPR, CAGR, standard deviation, beta, CAPM, Sharpe, duration | 35 | 4 |
| 11. Mutual Fund Scheme Performance | Tracking error, turnover, IRR, capture ratio, net returns | 20 | 4 |
| 12. Mutual Fund Scheme Selection | Rebalancing, TER drag, goal SIP, lump sum, fund choice | 20 | 4 |
Chapters 3, 4 are mostly theory, so they have no numerical set here.
Every formula below is used in the practice questions. Read the note column for conventions such as compounding period and sign.
| Measure | Formula | Note |
|---|---|---|
| Future value / present value | FV = PV × (1 + r)^n ; PV = FV / (1 + r)^n | r and n must use the same period (e.g. monthly rate with months); also inflated cost and zero-coupon price |
| CAGR | CAGR = (Ending value / Beginning value)^(1/n) − 1 | n in years; no interim cash flows |
| Effective annual yield | EAY = (1 + r/m)^m − 1 | m = compounding periods per year |
| Real return (Fisher) | Real = (1 + nominal) / (1 + inflation) − 1 | Approximation: nominal − inflation; today's value = Future amount / (1 + inflation)^n |
| Rule of 72 | Years to double ≈ 72 / return (%) | An approximation, most accurate near 6%–10% |
| Measure | Formula | Note |
|---|---|---|
| NAV per unit | NAV = (Market value of assets + Receivables − Liabilities) / Units outstanding | Net assets = NAV × Units |
| Units allotted | Units = Amount invested / Applicable NAV | Applicable NAV depends on the cut-off time |
| Sale and repurchase price | Sale price = NAV × (1 + Entry load %); Repurchase price = NAV × (1 − Exit load %) | Entry load is illustrative only; not permitted for new investments in India |
| Accrued interest | Accrued interest = Face value × Coupon × Days elapsed / 365 | Included in scheme assets when computing NAV |
| IDCW payout and ex-IDCW NAV | IDCW = Units × Face value × Rate ; Ex-IDCW NAV = Cum-IDCW NAV − IDCW per unit | Reinvested units = Units × IDCW per unit / Ex-IDCW NAV |
| Measure | Formula | Note |
|---|---|---|
| Total expense ratio | TER = Total expenses / Average net assets × 100 | Daily accrual = Net assets × TER / 365; embedded commission = Holding × (Regular TER − Direct TER) |
| Slab-wise TER | Expense = Σ (net assets in slab × slab TER) | Blended TER = Total expense / Net assets |
| Exit load | Exit load = Units within load period × NAV × Load % | Units are redeemed first-in-first-out unless stated |
| Trail commission | Trail = Average AUM × Annual trail rate × (Period / 1 year) | Break-even AUM = Annual cost / Trail rate |
| Measure | Formula | Note |
|---|---|---|
| Average cost per unit | Average cost = Total invested / Total units | Lower than the mean NAV for equal instalments |
| Future value of SIP (start of month) | FV = P × [((1 + i)^n − 1) / i] × (1 + i) | Drop the last (1 + i) factor for end-of-month instalments |
| SIP needed for a goal (end of month) | P = FV × i / [(1 + i)^n − 1] | i = monthly rate, n = months |
| SWP balance | Balance(t) = Balance(t−1) × (1 + i) − Withdrawal | Follow the order of growth and withdrawal stated |
| Equity weight for a target return | w = (Target − Rd) / (Re − Rd) | Rebalancing amount = Current equity − Target % × Portfolio |
| Retirement corpus | Corpus = Expenses × (1 + inflation)^n / Withdrawal rate | Years to a target: n = ln(Target / PV) / ln(1 + r) |
| Measure | Formula | Note |
|---|---|---|
| Capital gain | Gain = Units × (Sale price − Cost price) | FIFO matching for partial redemptions |
| Tax on capital gains | Tax = STCG × ST rate + (LTCG − Exemption) × LT rate | Rates, holding periods and exemption are stated in each question |
| Loss set-off | Net gain = Gain − Loss | Follow the set-off rules stated in the question; short-term loss can absorb either gain |
| IDCW and TDS | Net IDCW = IDCW − TDS rate × IDCW ; Additional tax = Slab tax − TDS | TDS applies only above the stated threshold |
| Measure | Formula | Note |
|---|---|---|
| Holding period return | HPR = (End value − Begin value + Income) / Begin value | |
| Annualised return and two-flow IRR | Annualised = (1 + HPR)^(365 / days) − 1 ; IRR: a(1 + r)² + b(1 + r) = Ending value | a invested at time 0, b at the end of year 1 |
| Geometric mean | GM = [Π (1 + r)]^(1/n) − 1 | Never above the arithmetic mean (Σ r / n) |
| Tracking difference | TD = Fund return − Index return | Tracking error = SD of these differences |
| Portfolio turnover | Turnover = Lower of (Purchases, Sales) / Average AUM × 100 |
| Measure | Formula | Note |
|---|---|---|
| Sample standard deviation | σ = √[ Σ (x − mean)² / (n − 1) ] | Population SD divides by n; CV = σ / Mean |
| Beta | β = Cov(scheme, market) / Var(market) = ρ × σs / σm | Portfolio beta = Σ weight × beta |
| Two-asset portfolio SD | σp = √[ w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2 ] | ρ = Cov / (σ1 σ2) |
| Maximum drawdown | MDD = (Peak − Trough) / Peak | The trough must come after the peak |
| CAPM | E(R) = Rf + β × (Rm − Rf) | |
| Sharpe and Treynor ratios | Sharpe = (Rp − Rf) / σp ; Treynor = (Rp − Rf) / β | Sharpe uses total risk, Treynor uses market risk |
| Jensen's alpha | α = Rp − [Rf + β (Rm − Rf)] | |
| Information ratio and capture ratio | IR = (Rp − Rbenchmark) / Tracking error ; Upside capture = Fund up-market return / Index up-market return × 100 |
| Measure | Formula | Note |
|---|---|---|
| Modified duration and price change | MD = Macaulay duration / (1 + y) ; ΔP/P ≈ − MD × Δy | Approximation for small yield changes |
| Approximate YTM | YTM ≈ [C + (F − P)/n] / [(F + P)/2] | |
| Weighted average maturity | WAM = Σ (Market value × Maturity) / Σ Market value |
Spoiler warning: if you want to test yourself first, take the tests above before reading the tables.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 1 | Purchasing power of money after inflation | Rs. 2,79,197 | Rs. 5,00,000 / (1.06)^10 = Rs. 2,79,197. |
| 1 | Rule of 72 - rate to double | 9.00% | 72 / 8 = 9.00%. |
| 2 | Units allotted for an investment | 1,355.014 units | Rs. 25,000 / Rs. 18.45 = 1355.014 units. |
| 2 | Value and unrealised gain on a holding | Rs. 24,000.00 | 4,000 × (Rs. 36.00 − Rs. 30.00) = Rs. 24,000.00. |
| 5 | SIP - units accumulated | 1,155.864 units | 10000/36 + 10000/32.4 + 10000/28.8 + 10000/45 = 1155.864 units. |
| 5 | Weighted average maturity of a debt portfolio | 3.30 years | (30×1 + 30×2 + 40×6) / 100 = 3.30 years. |
| 6 | Clawback of upfront commission | Rs. 6,000 | Redeemed = Rs. 6,00,000; clawback = Rs. 6,00,000 × 1.0% = Rs. 6,000. |
| 6 | Embedded commission in regular plan | Rs. 6,400 | Rs. 8,00,000 × (1.8% − 1.0%) = Rs. 6,400. |
| 7 | Redemption proceeds net of exit load | Rs. 22,176.00 | 800 × Rs. 28.00 × (1 − 1.0%) = Rs. 22,176.00. |
| 7 | Total assets from NAV, units and liabilities | Rs. 352.00 crore | Net assets = 34 × 10 = Rs. 340.00 crore; total assets = Rs. 340.00 crore + 12 = Rs. 352.00 crore. |
| 8 | Debt fund gains taxed at slab rate | Rs. 30,000 | Gain = 10,000 × (165 − 150) = Rs. 1,50,000; tax = Rs. 1,50,000 × 20% = Rs. 30,000. |
| 8 | Tax on two lots - short-term and long-term | Rs. 24,000 | STCG = Rs. 55,000 → tax Rs. 11,000; LTCG = Rs. 2,30,000 → taxable Rs. 1,30,000 → tax Rs. 13,000; total = Rs. 24,000. |
| 9 | Average cost of holding across purchases | Rs. 25.85 | Units = 10000/38 + 40000/30 + 50000/22 = 3869.219; Rs. 1,00,000 / 3869.219 = Rs. 25.85. |
| 9 | Closing units in a folio statement | Rs. 30,558.40 | Closing units = 1200.500 + 300.250 + 150.125 + 25.375 − 600.250 = 1076.000; value = 1076.000 × Rs. 28.40 = Rs. 30,558.40. |
| 10 | Geometric mean return | 15.14% | Product = 1.25 × 0.90 × 1.25 × 1.25 = 1.7578; 1.7578^(1/4) − 1 = 15.14%. |
| 10 | Jensen alpha | +2.20% | Required return = 6 + 0.8 × (12 − 6) = 10.80%; alpha = 13 − 10.80 = +2.20%. |
| 11 | Average AUM and expense ratio | 1.88% | Average AUM = 1960/4 = 490; 9.2 / 490 × 100 = 1.88%. |
| 11 | Net return from gross gains and expenses | 11.00% | (50 − 6) / 400 × 100 = 11.00%. |
| 12 | Age-based equity allocation | Rs. 7,00,000 | Equity % = 100 − 30 = 70%; amount = Rs. 10,00,000 × 70% = Rs. 7,00,000. |
| 12 | Corpus after cost of investing (TER drag) | Rs. 2,59,374 | Net return = 12% − 2.0% = 10%; Rs. 1,00,000 × (1 + 0.1000)^10 = Rs. 2,59,374. |
The second free test covers different topics and numbers from Test 1. The same spoiler warning applies.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 1 | Cumulative return over two years | -2.00% | 1.40 × 0.70 − 1 = -2.00%. |
| 1 | Real rate of return (exact relation) | 6.67% | 1.12 / 1.05 − 1 = 6.67%. |
| 2 | Fund size (AUM) from units and NAV | Rs. 1,022.40 crore | 24 crore × 42.6 = Rs. 1,022.40 crore. |
| 2 | Units allotted - applicable NAV (cut-off) | 1,071.237 units | Received at 4:05 p.m., so Tuesday's NAV Rs. 56.01 applies: Rs. 60,000 / Rs. 56.01 = 1071.237 units. |
| 5 | SIP average cost per unit | Rs. 41.73 | Units = 10000/44 + 10000/50 + 10000/40 + 10000/32 + 10000/48 = 1198.106; Rs. 50,000 / 1198.106 = Rs. 41.73. |
| 5 | SIP maturity value with constant monthly return | Rs. 4,35,076 | Rs. 10,000 × [(1.0100^36 − 1)/0.01] × (1 + 0.01) = Rs. 4,35,076. |
| 6 | Break-even AUM for a distributor | Rs. 4.80 crore | Annual cost = Rs. 4,80,000; AUM = Rs. 4,80,000 / 1.0% = Rs. 4.80 crore. |
| 6 | Trail commission for a quarter | Rs. 50,000 | Rs. 2,00,00,000 × 1.0% × 1/4 = Rs. 50,000. |
| 7 | NAV per unit from itemised assets and liabilities | Rs. 18.46 | Assets = 600 + 300 + 30 + 20 = 950; liabilities = 12 + 15 = 27; net = 923; NAV = 923 / 50 = Rs. 18.46. |
| 7 | Tiered TER - permissible expense in rupees | Rs. 36.80 crore | 500 × 2.40% + 250 × 2.15% + 1050 × 1.85% = Rs. 36.80 crore. |
| 8 | Capital gain on partial redemption - FIFO | Rs. 8,500 | 400 × (37 − 22) + 500 × (37 − 32) = Rs. 6,000 + Rs. 2,500 = Rs. 8,500. |
| 8 | ELSS deduction and tax saving | Rs. 30,000 | Eligible deduction = min(Rs. 2,50,000, Rs. 1,50,000) = Rs. 1,50,000; saving = Rs. 1,50,000 × 20% = Rs. 30,000. |
| 9 | Nominee-wise distribution of proceeds | Rs. 5,00,000 | Rs. 10,00,000 × 50% = Rs. 5,00,000. |
| 9 | Value left after a redemption request in rupees | Rs. 54,000 | 3,500 × Rs. 24.00 = Rs. 84,000; less Rs. 30,000 = Rs. 54,000. |
| 10 | Expected return from scenarios | 11.00% | 0.3×(20%) + 0.5×(12%) + 0.2×(-5%) = 11.00%. |
| 10 | Maximum drawdown | 13.04% | Worst fall: peak 46 to trough 40: (46 − 40) / 46 = 13.04%. |
| 11 | Annualised outperformance from absolute returns | 4.51% | CAGR scheme = 1.90^(1/3) − 1 = 23.86%; benchmark = 1.70^(1/3) − 1 = 19.35%; difference = 4.51. |
| 11 | Rolling returns - frequency of outperformance | 62.5% | 5 / 8 × 100 = 62.5%. |
| 12 | Emergency fund requirement | Rs. 5,40,000 | (Rs. 40,000 + Rs. 20,000) × 9 = Rs. 5,40,000. |
| 12 | Lump sum needed today for a goal | Rs. 3,10,461 | Rs. 5,00,000 / (1.10)^5 = Rs. 3,10,461. |
Yes, some. The V-A syllabus includes NAV and expense-ratio arithmetic, exit loads and units allotted, capital-gains tax, and return and risk measures such as CAGR, standard deviation, beta and the Sharpe ratio. NISM does not publish how many questions in the paper are numerical, so practise the formulas until they are automatic.
NISM's general candidate instructions say candidates may bring their own physical calculator, which must be silent and have no connectivity, and that rough sheets are provided by the invigilator. Confirm the rules in your registration or admit instructions before exam day.
The exam has 100 multiple-choice questions of 1 mark each. The pass mark is 50 out of 100 (50%). NISM Series V-A has no negative marking, so unanswered and wrongly answered questions both score zero.
You get 1 mark for each correct answer. NISM Series V-A has no negative marking, so a wrong answer costs nothing and skipped questions score zero.
Yes. Two 20-question numerical tests (40 solved questions) are free with a free BullWiser account, which takes a few seconds to create. The full bank of 200 numerical questions, served 25 at a time and favouring questions you have not seen, comes with BullWiser V-A mock access, a one-time payment of Rs 199 per series.
Yes. Every question in the two free tests shows the correct answer, the formula, the step-by-step working and the common mistake when you finish. The solutions are also published on this page, so you can read them without taking the test.
No. BullWiser prepared them from the standard formulas taught in the NISM workbook, and each has a worked explanation. Names of people, companies and funds are fictional. BullWiser is not affiliated with NISM.
Take the full-length V-A mock, read the V-A notes and question bank, or start with the chapters that have the most numericals: NAV, Total Expense Ratio and Pricing, Risk, Return and Performance of Funds, Taxation.
Preparing for another paper? Numerical practice is also available for: